Compressed sensing (“CS”), an acceleration technique of growing importance in magnetic resonance imaging (“MRI”), can be used to reconstruct high-quality images from data sampled well below the Nyquist rate. To improve accuracy and decrease data acquisition time, the choice of sampling pattern is an important design element in CS. Variable-density random k-space sampling patterns are particularly effective for three-dimensional (“3D”) Cartesian sampling, where there is flexibility in choosing ky and kz phase encoding positions [1, 2]. The design of two-dimensional (“2D”) sampling patterns of high acceleration is more challenging.
Adcock et al. recently developed a framework that describes MRI as both asymptomatically sparse and asymptomatically incoherent, and using this framework they designed an optimal multilevel random sub-sampling scheme [3]. While helpful in bridging the gap between existing CS theory and real-world application, the sub-sampling scheme in Adcock may be limited in its application to 2D CS MRI with high acceleration.
It is with respect to these and other considerations that the various embodiments described below are presented.